JEE Main · 2022 · 26 Jun 2022 · Shift 1 · Laws of Motion

WhatsApp Email

A ball is released from rest from point P of a smooth semi-spherical vessel as shown in figure. The ratio of the centripetal force and normal reaction on the ball at point Q is A while angular position of point Q is

α

with respect to point P. Which of the following graphs represent the correct relation between A and

α

when ball goes from Q to R ?

(A)(see structure)
(B)(see structure)
(C)(see structure)
✓ Correct
(D)(see structure)

Answer: (C)

Solution

Using energy conservation from P to Q:

v^{2} = 2 g R sin α

. At Q, applying Newton's second law in the radial direction:

N - m g sin α = \frac{m v ^{2}}{R} = 2 m g sin α

. Therefore

N = 3 m g sin α

. The centripetal force is

\frac{m v ^{2}}{R} = 2 m g sin α

. The ratio

A = \frac{centripetal force}{N} = \frac{2 m g s i n α}{3 m g s i n α} = \frac{2}{3}

, which is constant. The correct graph shows A as a horizontal line (constant).

JEE Main · 2022 · 26 Jun 2022 · Shift 1 · Single correct option

Practise more: all JEE Main PYQs on Laws of Motion →

JEE Main · 2022 · 26 Jun 2022 · Shift 1 · Laws of Motion

Solution

More JEE Main questions on Laws of Motion